# Revealed norm obedience

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## Abstract

We study a rational decision maker who obeys social norms. In our setup norms prescribe choices in some decision problems. The decision maker obeys norms in situations to which they apply and otherwise maximizes her preference relation. We characterize the class of choice functions that can be explained by this decision procedure, relate this procedure to other decision procedures in the literature, and engage in welfare considerations.

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## Notes

1. Abusing notation, we will write $$C\left( x_{1},\dots ,x_{k}\right)$$ instead of $$C\left( \left\{ x_{1},\dots ,x_{k}\right\} \right)$$ for $$x_{j}\in X,\,j=1,\dots ,k$$.

2. That is, $$\succ$$ is asymmetric, transitive, and satisfies the following completeness property: $$\forall x,y\in X,x\ne y$$ it holds $$x\succ y$$ or $$y\succ x$$.

3. To see the details, assume that $$X=\left\{ a,b,c\right\}$$ and $$C$$ is induced by the sequence of rationales $$\left( P_{i}\right) _{i\in \mathbb {N}}$$. W.l.o.g. we can assume $$P_{1}\ne \varnothing$$. $$C\left( a,b,c\right) =b$$ implies $$\left( a,b\right) \notin P_{1}$$ and $$\left( c,b\right) \notin P_{1}$$. $$C\left( a,b\right) =a$$ implies $$\left( b,a\right) \notin P_{1}$$ and $$C\left( a,c\right) =a$$ implies $$\left( c,a\right) \notin P_{1}$$. Hence $$\left( a,c\right) \in P_{1}$$ or $$\left( b,c\right) \in P_{1}$$. Either way we have $$\gamma _{P_{1}}\left( a,b,c\right) =\gamma _{P_{1}}\left( a,b\right)$$, contradicting $$C\left( a,b,c\right) \ne C\left( a,b\right)$$.

4. Note that Cherepanov et al. (2013) actually derive In from some deeper structure modelling the use of rationalizations in decision making. However for our purposes this derivation is not of interest.

## References

• Baigent N, Gaertner W (1996) Never choose the uniquely largest. A characterization. Econ Theory 8:239–249

• Bardsley N (2008) Dictator game giving: altruism or artefact? Exp Econ 11:122–133

• Bernheim DB, Rangel A (2009) Toward choice-theoretic foundations for behavioral welfare economics. Q J Econ 124:51–104

• Cherepanov V, Feddersen T, Sandroni A (2013) Rationalization. Theor Econ 8:775–800

• Darley J, Latane B (1968) Bystander intervention in emergencies. Diffusion of responsibility. J Personal Soc Psychol 8:377–383

• Diekmann A (1985) Volunteers dilemma. J Confl Resolut 29:605–610

• Durkheim E (1997) The division of labour in society. Free Press, New York

• Esser H (2001) Soziologie. Spezielle Grundlagen. Sinn und Kultur. Campus, Frankfurt am Main

• Gaertner W, Xu Y (1999a) On rationalizability of choice functions: a characterization of the median. Soc Choice Welf 16:629–638

• Gaertner W, Xu Y (1999b) On the structure of choice under different external references. Econ Theory 14:609–620

• Gaertner W, Xu Y (1999c) Rationality and external reference. Ration Soc 11:169–185

• Kroneberg C (2005) Die Definition der Situation und die variable Rationalität der Akteure. Ein allgemeines Modell des Handelns. Z fr Soziol 34:344–363

• Kroneberg C, Heintze I, Mehlkop G (2010a) The interplay of moral norms and instrumental incentives in crime causation. Criminology 48:259–294

• Kroneberg C, Yaish M, Stocke V (2010b) Norms and rationality in electoral participation and in the rescue of jews in WWII: an application of the model of frame selection. Ration Soc 22:3–36

• Lleras J, Masatlioglu Y, Nakajima D, Ozbay E (2010) When more is less: limited consideration. Working Paper

• Manzini P, Mariotti M (2007) Sequentially rationalizable choice. Am Econ Rev 97:1824–1839

• Manzini P, Mariotti M (2012) Choice by lexicographic semiorders. Theor Econ 7:1–23

• Masatlioglu Y, Nakajima D, Ozbay EY (2012) Revealed attention. Am Econ Rev 102:2183–2205

• Masatlioglu Y, Ok EA (2005) Rational choice with status-quo bias. J Econ Theory 121:1–29

• Mayerl J (2010) Die Low-Cost-Hypothese ist nicht genug. Eine empirische Überprüfung von Varianten des Modells der Frame-Selektion zur besseren Vorhersage der Einflussstärke von Einstellungen auf Verhalten. Z fr Soziol 39:28–59

• Parsons T (1968) The structure of social action. Free Press, New York

• Quandt M, Ohr D (2004) Worum geht es, wenn es um nichts geht? Zum Stellenwert von Niedrigkostensituationen in der Rational Choice-Modellierung normkonformen Handelns. Kölner Zeitschrift für Soziologie und Sozialpsychologie 56:683–707

• Rubinstein A (1998) Modeling bounded rationality. MIT Press, Cambridge

• Rubinstein A, Salant Y (2006) A model of choice from lists. Theor Econ 1:3–17

• Rubinstein A, Salant Y (2012) Eliciting welfare preferences from behavioural data sets. Rev Econ Stud 79:375–387

• Rubinstein A, Zhou L (1999) Choice problems with a ‘reference’ point. Math Soc Sci 37:205–209

• Salant Y, Rubinstein A (2008) (A, f): choice with frames. Rev Econ Stud 75:1287–1296

• Samuelson PA (1938) A note on the pure theory of consumers’ behavior. Econometrica 5:61–71

• Sandbu ME (2007) Fairness and the roads not taken: an experimental test of non-reciprocal set-dependence in distributive preferences. Games Econ Behav 61:113–130

• Sandroni A (2011) Akrasia, instincts, and revealed preferences. Synthese 181:1–17

• Tversky A (1972) Elimination by aspects: a theory of choice. Psychol Rev 79:281–299

• Weber M (1978) Economy and society, University of California Press, Berkeley

## Author information

Authors

### Corresponding author

Correspondence to Andreas Tutić .

Thanks to Bea, who suggested the term ‘obedience’, and two referees for good advice.

## Appendix

### Appendix

Proposition 5

Consider the following choice function: $$C_{1}\left( a,b,c\right) =a$$, $$C_{1}\left( a,b\right) =a$$, and $$C_{1}\left( b,c\right) =C_{1}\left( a,c\right) =c$$. $$C_{1}$$ satisfies OD but not AC.

Consider $$C_{2}\left( a,b\right) =C_{2}\left( a,d\right) =a$$, $$C_{2}\left( a,c\right) =C_{2}\left( c,d\right) =c$$, $$C_{2}\left( b,c\right) =C_{2}\left( b,d\right) =b$$. Letting $$C_{2}\left( a,b,c\right) =C_{2}\left( b,c,d\right) =b$$, $$C_{2}\left( a,b,d\right) \!=\!C_{2}\left( a,b,c,d\right) =a$$, and $$C_{2}\left( a,c,d\right) =c$$, we observe that $$C_{2}$$ satisfies AC, but fails OD with respect to $$\left\{ a,b,c,d\right\} ,\left\{ a,b,c\right\}$$, and $$\left\{ a,b\right\}$$.

Let $$C_{3}\left( a,b,c\right) =C_{3}\left( a,b\right) =a$$, $$C_{3}\left( b,c\right) =b$$, and $$C_{3}\left( a,c\right) =c$$ meets OD but defys NBC. On the other hand, $$C_{4}\left( S\right) =C_{2}\left( S\right)$$ for all $$S\in \mathbb {X}\backslash \left\{ \left\{ a,c\right\} \right\}$$ and $$C_{4}\left( a,c\right) =a$$ satisfies NBC, but violates OD.

Let $$C_{5}\left( a,b,c,d\right) =C_{5}\left( a,b,d\right) =C_{5}\left( a,c,d\right) =C_{5}\left( a,d\right) =a$$, $$C_{5}\left( a,b,c\right) =C_{5}\left( b,c,d\right) =b$$, $$C_{5}\left( a,b\right) =C_{5}\left( b,d\right) =b$$, and $$C_{5}\left( b,c\right) =C_{5}\left( a,c\right) =C_{5}\left( c,d\right) =c$$. $$C_{5}$$ satisfies WW, but violates OD with respect to $$\left\{ a,b,c,d\right\} ,\left\{ a,b,c\right\}$$, and $$\left\{ b,c\right\}$$.

Section 3.1

Consider the following semiorders: $$P_{1}=\left\{ \left( d,b\right) ,\left( d,c\right) \right\}$$, $$P_{2}=\left\{ \left( a,d\right) \right\}$$, $$P_{3}=\left\{ \left( a,c\right) \right\}$$, $$P_{4}=\left\{ \left( b,a\right) \right\}$$, and $$P_{5}=\left\{ \left( c,b\right) \right\}$$. These semiorders induce choices $$C\left( a,b,c,d\right) =a$$, $$C\left( a,b,c\right) =b$$, and $$C\left( b,c\right) =c$$, violating OD.

Proposition 7

$$a\succ b\succ c\succ d$$ and $$\mathcal {N=}\left\{ \left( b,\left\{ a,b\right\} \right) ,\left( b,\left\{ b\right\} \right) ,\left( c,\left\{ a,c\right\} \right) ,\left( c,\left\{ c\right\} \right) \right\}$$ induce a choice function $$C^{\succ ,\mathcal {N}}$$ that violates SH with respect to $$\left\{ a,b\right\}$$ and $$\left\{ a,c\right\}$$.

Proposition 9

$$C_{5}$$ satisfies NBCC and violates OD.

Proposition 10

The following choice function satisfies OD but violates LCAW with respect to the set $$\left\{ a,b\right\}$$: $$C\left( a,b,c,d\right) =C\left( a,c\right) =c$$, $$C\left( a,b,c\right) =C\left( a,b\right) =C\left( b,c\right) =b$$, $$C\left( a,c,d\right) =C\left( b,c,d\right) =C\left( a,d\right) =C\left( b,d\right) =C\left( c,d\right) =d$$, and $$C\left( a,b,d\right) =a$$.

The following filter $$\Gamma$$ satisfies In and Ir: $$\Gamma \left( S\right) =S$$ for all $$S\in \mathbb {X}$$ with the exceptions $$\Gamma \left( a,b,c,d\right) =\Gamma \left( a,c,d\right) =\Gamma \left( b,c,d\right) =\left\{ c,d\right\}$$, $$\Gamma \left( a,b,c\right) =\left\{ b,c\right\}$$. Together with $$a\succ b\succ c\succ d$$ the filter induces a choice function that violates OD with respect to $$\left\{ a,b,c,d\right\} ,\left\{ a,b,c\right\}$$, and $$\left\{ a,b\right\}$$.

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Tutić , A. Revealed norm obedience. Soc Choice Welf 44, 301–318 (2015). https://doi.org/10.1007/s00355-014-0830-y